The visitors had enjoyed the better of the opening exchanges despite losing experienced striker Paul Shaw to injury on 17minutes, with his replacement, on-loan Sheffield United man Jonathan Forte causing problems with his pace.
Blackpool only forced Rotherham keeper Gary Montgomery into one serious save before the interval, which came when John Murphy squared for the unmarked Keith Southern, whose goal-bound shot was tipped over the bar.
The major moment of controversy arrived just before the break when Butler caught Wood in the face. The referee initially did nothing, but had the offence pointed out by the fourth official and had little choice but to show a red card.
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The second half saw Blackpool begin to press but Montgomery saved his side with a brilliant stop from Peter Clarke, who had reacted first to a cross from substitute Simon Wiles.
Forte and the hard-working Michael Keane created chances to earn what would have been a deserved victory for the ten men, but could not find a finish.